Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3549}(2978,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dq
\(\chi_{7098}(131,\cdot)\) \(\chi_{7098}(521,\cdot)\) \(\chi_{7098}(1067,\cdot)\) \(\chi_{7098}(1223,\cdot)\) \(\chi_{7098}(1613,\cdot)\) \(\chi_{7098}(1769,\cdot)\) \(\chi_{7098}(2159,\cdot)\) \(\chi_{7098}(2315,\cdot)\) \(\chi_{7098}(2861,\cdot)\) \(\chi_{7098}(3251,\cdot)\) \(\chi_{7098}(3407,\cdot)\) \(\chi_{7098}(3797,\cdot)\) \(\chi_{7098}(3953,\cdot)\) \(\chi_{7098}(4343,\cdot)\) \(\chi_{7098}(4499,\cdot)\) \(\chi_{7098}(4889,\cdot)\) \(\chi_{7098}(5045,\cdot)\) \(\chi_{7098}(5435,\cdot)\) \(\chi_{7098}(5591,\cdot)\) \(\chi_{7098}(5981,\cdot)\) \(\chi_{7098}(6137,\cdot)\) \(\chi_{7098}(6527,\cdot)\) \(\chi_{7098}(6683,\cdot)\) \(\chi_{7098}(7073,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{7}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(6527, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) |